In an arithmetic progression of ten terms, the extremes add up to 22 and the product of the third and fourth terms is 48. Calculate the value of those terms.

Let's denote the first term of the arithmetic progression as a and the common difference as d .

1. The sum of the extremes:
Given that the first term plus the tenth term equals 22, we have
a + (a + 9d) = 22
2a + 9d = 22
2a = 22 - 9d
a = 11 - \frac{9d}{2}

2. The product of the third and fourth terms:
The third term is a + 2d and the fourth term is a + 3d .
Given that the product of the third and fourth terms is 48, we have
(a + 2d)(a + 3d) = 48


solvinf equation we get

Answer: d = 2 and a=2 .